Poincare recurrence and intermittent loss of quantum Kelvin wave cascades in quantum turbulence

TL;DR

This paper introduces a quantum lattice gas algorithm for Bose-Einstein condensates, revealing short Poincare recurrence times and detailed spectral behaviors of quantum turbulence, including Kelvin wave cascades and their intermittent loss.

Contribution

It develops a novel quantum lattice gas method for BECs and uncovers new phenomena like short Poincare recurrence and intermittent Kelvin wave cascade loss in quantum turbulence.

Findings

Short Poincare recurrence times for certain initial conditions.

Spectral analysis confirms classical and quantum cascade regions.

Intermittent loss of Kelvin wave cascade observed in vortex dynamics.

Abstract

The evolution of the ground state wave function of a zero-temperature Bose-Einstein condensate (BEC) is well described by the Hamiltonian Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved unitary collision-streaming operators, a quantum lattice gas algorithm is devised which on taking moments recovers the Gross-Pitaevskii (GP) equation in diffusion ordering (time scales as square of length). Unexpectedly, there is a class of initial conditions in which their Poincare recurrence is extremely short. Further it is shown that the Poincare recurrence time scales with diffusion ordering as the the grid is increased. The spectral results of Yepez et.al. [1] for quantum turbulence are corrected and it is found that it is the compressible kinetic energy spectrum that exhibits the 3 cascade regions: a small k classical Kolmogorov k^(-5/3) spectrum, a steep semi-classical cascade region, and a large k quantum Kelvin wave cascade k^(-3) spectrum. The incompressible kinetic energy spectrum exhibits basically a single cascade power law of k^(-3). For winding number 1 linear vortices it is also shown that there is an intermittent loss of Kelvin wave cascade with its signature seen in the time evolution of the kinetic energy, the loss of the k^(-3) spectrum in the incompressible kinetic energy spectrum as well as the minimization of the vortex core isosurfaces that inhibits the Kelvin wave cascade.